Statistical mechanics of image restoration and error-correcting codes

TL;DR

This paper applies statistical mechanics to analyze image restoration and error-correcting codes, revealing optimal parameters and performance limits through theoretical models and simulations.

Contribution

It introduces a statistical-mechanical framework linking image restoration and error correction to spin glass models, providing exact solutions and parameter estimation insights.

Findings

Optimal restoration performance occurs at specific parameter values.

Infinite-range model solutions guide parameter estimation.

Monte Carlo simulations validate applicability to 2D image restoration.

Abstract

We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the quality of restoration/decoding is maximized at a specific set of parameter values determined by the source and channel properties. For image restoration in mean-field system a line of optimal performance is shown to exist in the parameter space. These results are illustrated by solving exactly the infinite-range model. The solutions enable us to determine how precisely one should estimate unknown parameters. Monte Carlo simulations are carried out to see how far the conclusions from the infinite-range model are applicable to the more realistic two-dimensional case in image restoration.